Question

Identify the correct statement regarding an equipotential surface:

• A. An equipotential surface and electric line of force intersect at an angle of ${90}^{\circ }$.
• B. An equipotential surface and electric line of force intersect at an angle of ${60}^{\circ }$.
• C. An equipotential surface and electric line of force intersect at an angle of ${45}^{\circ }$.
• D. An equipotential surface and electric line of force never intersect each other.

Answer 1

The correct option is A An equipotential surface and electric line of force intersect at an angle of ${90}^{\circ }$.


As shown in figure, the electric field lines represent a uniform electric field.

Let us consider two points $A$ and $B$ on the equipotential surface.

Potential difference between those two points is given by

$V_B-V_A=\underset{A}{\overset{B}{\int }}\overrightarrow{E}\cdot \overrightarrow{dl}$

Since, $V_B=V_A$ we can write that,

$\overrightarrow{E}\cdot \overrightarrow{dl}=0$

$\Rightarrow \overrightarrow{E}\perp \overrightarrow{dl}$

We know that, Electric lines of force will be along the $\overrightarrow{E}$ for a uniform electric field. (Electric lines of force are tangential to $\overrightarrow{E}$, thus electric lines of force intersect the equipotential surfaces at ${90}^{\circ }$.

Hence, option (c) is the correct answer.

why this question? Tip: Electric line of forces represents the direction of trajectory for +ve charge in an electric field and is always tangential to $\overrightarrow{E}$ at any point.